The PTT Model in Hip Joint Replacement: Shock Loading

Abstract

The Phan-Thien Tanner (PTT) model is one of the most widely used rheological models. It can properly describe all the common characteristics of viscoelastic non-Newtonian fluids. Synovial fluid of human joints, which also lubricates artificial joints, is well known to be highly viscoelastic. Thus it is reasonable to attempt to describe such joint behavior using non-Newtonian flow models. Modeling the geometry of the total hip replacement, the PTT model is applied in spherical coordinates to a thin confined fluid film. As an illustrative problem, the case of a sudden impulsive start of simple squeezing motion is solved, similar to landing on one’s feet after a vertical jump. The phenomena of shear thinning, stress relaxation, and stress overshoot are all exhibited.